Hasni Dyah Kurniawati, Saefudin Saefudin, fernando julio parera, Nurlyana Puspitasari ¡ 7 authors
<ns3:p> Research background In recent decades, venture capital (VC) has increasingly incorporated sustainability principles, reflecting the global shift toward environmentally and socially responsible investment. The alignment of VC with sustainability goals responds to the climate crisis, technological transformation, and social expectations for ethical finance. However, research on the VCâsustainability nexus remains fragmented across disciplines, requiring systematic mapping to clarify key trends and research gaps. This study aims to map the global evolution of VC research within the context of sustainability. It identifies publication trends, collaboration patterns, main thematic clusters, and emerging research areas to provide an integrated understanding of this growing field. Methods A mixed-methods bibliometric analysis was conducted using data retrieved from the Scopus database for the period 2002â2025. Analytical tools including <ns3:italic>RStudio and VOSviewer</ns3:italic> were applied to examine publication dynamics, co-authorship networks, and conceptual structures. The SPAR-4-SLR protocol was adopted to ensure methodological transparency and rigor. Discussion Results show that international collaborationâparticularly among China, the United States, and the United Kingdomâdrives sustainable innovation in the VC ecosystem. Three main clusters were identified: the theoretical evolution of VC, long-term policy and economic frameworks, and VCâs role in green entrepreneurship and sustainable technology. Research on emerging themes such as decentralized finance (DeFi), machine learning, and risk modeling remains limited. This study adds value by offering a systematic overview of the intellectual landscape and highlighting future research directions to strengthen VCâs contribution to global sustainability. </ns3:p>
The division between traditional finance (TradFi) and decentralized finance (DeFi) continues tohinder seamless capital mobility across ecosystems. RealâTime Payment Systems (RTPS) achievenearâinstant fiat settlements, yet bridging these assets into blockchain environments remainsdependent on fragmented, highâlatency, and centralized gateways. This gap limits the naturalstrengths of both worlds, especially speed and efficiency. Based on the publish/subscribe model, theEDSP protocol operates as a decentralized oracle system that allows for synchronization of stateupdates between two separate ledgers. This protocol will allow smart contracts to initiate fiatpayments and bank payment systems to trigger corresponding blockchain settlement actions. Themodel stresses cryptographic protections against oracle tampering through multi-party authenticationand zero-trust routing methodologies. A simulation of latency shows that an event-driven architectureis capable of resolving the deterministic nature of TradFi operations and the probabilistic aspect ofblockchain networks. Incorporating compliance events into the settlement process enables institutionsto meet their demands for regulatory and transparency obligations. This article sets a roadmap forfuture liquidity bridging models based on a secure, scalable, and compliant approach to bridgingecosystems. This article proves the value that event-driven models bring to the table in terms ofinterconnectivity and liquidity, which will allow institutional-level interactions to take place withinfiat and decentralized networks.
Cloud providers need to report to their customers what carbon emissions have arisen from their use of computing resources, so that customers can include them in their own mandated emissions reporting. At present, these reports are neither verifiable nor audited. We show how a data centre operator can produce cryptographic zero-knowledge proofs to each customer that the emissions reported to that customer are accurate, without the customer being able to learn sensitive information about the data centre operator or other customers. Our approach is scalable, costing a data centre operator with one million customers an estimated $150 USD per month plus $0.01 USD for each customer who requests a verifiable emissions report. For customers, a proof is 37 KiB in size, and verifying it takes less than a second. By making emissions reports more trustworthy, we hope to give companies and policymakers the data they need to push towards decarbonisation.
A current, urgent problem is whether the price behavior pattern of significant quantities of digital assets reflects a single direction trend line or multiple phases that exhibit different structures, adjusted inter-asset relationship differences, and changes in management systems, given the growing importance of digital assets in investment portfolios and collateral holdings, exchange-traded funds (ETFs), new forms of financial activities, and system risks over the period from 2020 through 2025. Because of this periodâs post-pandemic recovery, speculative overextension, sharp decline, stabilization, and the re-entry of large-scale institutions into practice, these changes in prices are more clearly identified under such a context. Empirically, this study integrates descriptive statistics, rolling volatility analysis, augmented DickeyâFullerâs unit-root test, segmented trend regression model with structural breaks, and vector autoregression (VAR) for return interactions. Based on these bases, both Bitcoin and Ethereum have demonstrated a relatively strong direction of continuous appreciation, together with quite considerable regime-specific instability. The log-price series is non-stationary, but the daily return series is stationary; so a level model is appropriate for medium-term trend analysis, and returns-based models can be applied more flexibly at shorter timespans. The segmented trend-regression analysis shows that close to peaks, such as those that occurred in 2021 for a long period, the 2022 correction, and the resumption of investment in 2024, are relatively distinct from the overall linear change pattern across all time periods. Both Bitcoin and Ethereum display pronounced contemporaneous co-movement, but they show no substantial lags via VAR or Granger causality tests conducted in the context of time-varying parameters. This study employs an integrated empirical research approach based on various perspectives to explore the long-term structural adjustment and near-instantaneous cross-market relationship dynamics, as well as regulatory mechanisms within a systemic context.
This research investigates critical challenges in Transformer-based smart contract auditing systems, with a specific focus on inference instability and class imbalance in CodeBERT-based binary vulnerability classification. Layer-2 blockchain networks introduce highly complex architectures that increase the risk of smart contract exploits, where traditional static analysis tools such as Slither often produce large volumes of noisy, rule-based alerts. Recent advancements in pre-trained Transformer models, particularly CodeBERT, have demonstrated strong capabilities in semantic code understanding and vulnerability detection. However, during deployment of a fine-tuned CodeBERT-base model, we observe significant performance and stability issues. Initial inference experiments show a 100% false-positive rate, primarily attributed to severe class imbalance in the slither-audited-smart-contracts dataset and model sensitivity to specific smart contract patterns such as raw Ether transfer functions. In addition, system-level execution profiling reveals a silent segmentation fault during model initialization. Further investigation using Windows OS logs identifies dependency conflicts between PyTorch and PyArrow (via Hugging Face Datasets), particularly related to C++ DLL load-order issues. Experimental analysis demonstrates that modifying dependency import order, prioritizing PyArrow initialization, and enforcing strict model.eval() state management significantly improves inference stability. These findings highlight important architectural and deployment considerations for Transformer-based blockchain security systems and provide practical insights for improving the robustness of automated smart contract auditing pipelines in Layer-2 Web3 ecosystems.
Dr. B. Indira Reddy, Naga Siva Jyothi Kompalli, Dr. Rohita yamaganti, CH Sai Saketh ¡ 6 authors
The ongoing digital evolution in the healthcare sector has increased the demand for reliable and secure systems to manage medical records. Conventional centralized storage methods are vulnerable to security threats such as data breaches, unauthorized usage, and potential data alteration, which can compromise patient confidentiality and data integrity. To overcome these challenges, this work presents a blockchain-enabled medical record management system designed to provide secure and tamper-resistant data storage. The proposed system is implemented as a decentralized web application, utilizing React.js for the user interface and Web3.js or Ethers.js to enable interaction with the blockchain network. Smart contracts written in Solidity are deployed on the Ethereum platform to handle record management and enforce strict access permissions. User authentication is facilitated through MetaMask, ensuring a secure and decentralized method of identity verification. Healthcare information, including patient records, diagnoses, prescriptions, and treatment details, is maintained on the blockchain to guarantee transparency and immutability. The system empowers patients by allowing them to control access to their data, including granting and revoking permissions for healthcare providers. Tools such as Truffle and Ganache are used during development for efficient testing and deployment. In summary, the proposed solution improves data security, privacy, and accessibility, offering a dependable and scalable approach for managing healthcare records in modern digital environments.
PrismEco is the showcase demonstration of the Prism Ecosystem. Where the other component demos each illustrate one capability in isolation, PrismEco shows the complete authentication triangle in a single flow: biometric authentication via WebAuthn, a Zero-Knowledge Proof generated in the browser, and NFC presence verification via a physical tag. This technical note follows a single user through the complete login flow on prismeco.globalsecurity.nu. At each step, it documents what the server receives and what it does not receive. The goal is to make visible what is structurally invisible by design: that a working authentication system can process a login without ever knowing who the user is. The three factors are verified independently and must all succeed for the session to open. No single factor is sufficient on its own. The combination is structurally resistant to remote attacks: an attacker would need to compromise biometrics, the device, and physical proximity simultaneously. The complete authentication triangle has been proven in a working PoC as of 12 June 2026. WebAuthn registration and login, ZKP generation and server-side verification (proven 10 June 2026), and NFC tap confirmation with RELAY_TOKEN verification (proven 12 June 2026) all function as an integrated flow on live infrastructure at prismeco.globalsecurity.nu. Screenshots in this document are taken from the live running demonstration. All claims are classified by status: proven in PoC, follows from open standard, or architectural design choice. Part of the Prism Ecosystem. Full technical architecture: The Prism Protocol, Invention Disclosure v20, DOI: 10.5281/zenodo.20029291.
We present a convolutional variational autoencoder for cryptocurrency implied-volatility surfaces, together with a deployable predictor that combines it with a quadratic smile re-fit through a deterministic per-tenor routing rule. Trained on 6,034 fully-filled hourly Binance Options surfaces of BTC and ETH spanning May-October 2023 and parameterised on a common $6 \times 7$ tenor-delta grid, the model attains a hidden-cell surface-completion RMSE in the 0.94-1.56 vol-point range across both markets and mask rates 10-50%. The hybrid predictor attains 0.83 vol points at 50% masking against 7.00 for the smile re-fit alone, an eightfold reduction obtained at no additional inference cost. Under structurally-correlated hole patterns that emulate the withdrawal of an entire tenor of strikes, the smile re-fit incurs 9.6-13.1 vol points of error while the learned model remains at 1.5-1.9, isolating a regime in which the generative model is the only viable predictor. Joint training on BTC and ETH improves the in-distribution model on both markets by 9-27% relative to the better-performing single-symbol counterpart, indicating a substantially shared vol-surface manifold across the two largest cryptocurrencies over the observation window. The hybrid is calendar- and butterfly-arbitrage-free at the listed strikes, a property that the parametric smile re-fit alone fails at high mask rates. The per-snapshot reconstruction error of the trained model flags the late-October ETF-anticipation rally and the August $17$, $2023$ flash crash as elevated-error periods without supervision. All training and evaluation infrastructure is released to support reproducible follow-on work.
Cryptocurrency markets are prone to violent, synchronised drawdowns, challenging the claim that a basket of crypto-assets offers genuine internal diversification. Because standard covariance-based metrics fail to capture asymptotic tail dependence, they systematically understate systemic risk and overstate diversification benefits precisely when markets crash. This study maps the conditional dependence structure of the cryptocurrency market directly in the joint tails, isolating direct extremal linkages from those mediated by the rest of the system. We analyse the daily returns of the thirteen largest cryptocurrencies over a sequence of 89 overlapping windows spanning late 2021 to 2025. We apply dynamic HĂźsler-Reiss graphical models of extremes, estimated separately for joint crashes and rallies, and benchmark them against a Gaussian graphical model of ordinary co-movement. The results reveal a near-complete and stable lower-tail graph, an upper tail that thins over time to re-form sectoral structures, and the dissolution of ordinary token categories into a single block anchored by a Bitcoin-Ethereum core. These findings imply that intra-crypto diversification fails on the downside, standard risk models underestimate market-wide crash probabilities by roughly eight-fold, and dynamic extremal graphs offer a superior tool for systemic risk monitoring.
Rowdy Chotkan, Bulat Nasrulin, Johan Pouwelse, JĂŠrĂŠmie Decouchant
Distributed systems handle adversarial nodes through redundancy, which imposes a significant performance overhead. In blockchain systems, Byzantine fault-tolerant state-machine replication (BFT-SMR) is the replicated service that totally orders client transactions before execution. While prior research has primarily focused on designing novel consensus algorithms with improved performance, recent studies have shown that further gains can be achieved through configuration optimization. More precisely, replicas can monitor network latency to dynamically assign the leader role and tune voting weights, thereby improving consensus performance. However, we identify three vulnerabilities in this process that Byzantine nodes can exploit. To address these weaknesses, we propose Beware, a reconfiguration framework that filters out falsified latency reports, computes robust weight distributions, and applies machine learning to converge towards Byzantine-resilient configurations. Our evaluation shows that Beware reduces consensus latency by up to 45% compared to existing solutions.
Modern blockchain state management faces a critical scalability bottleneck: maintaining cryptographic commitments over hundreds of millions of entries becomes computationally prohibitive. Ethereum's transition to Verkle Trees: polynomial commitment accumulators reducing proof sizes from O(width * depth) to O(depth) via constant-size IPA vector commitments, is a critical step toward stateless operation. Yet, current implementations exhibit pathological characteristics that burden home validators. We identify four inefficiencies in the reference go-verkle implementation \cite{kaur2025goverkle, kaur2025goethereum}: (1) phantom node creation during non-existent account deletion; (2) 64-byte database keys triggering excessive LSM-tree compaction; (3) redundant memory copying in proof deserialization; (4) a Proof of Absence wire format incompatibility causing non-deterministic serialization. We present Fractional Verkle Trees (FVT), a hypertree decomposition partitioning global state into N independent sub-accumulators coordinated by a Merkle commitment tree, achieving improved cache locality, zero-lock-contention goroutine-parallel commitment computation, and faster root recomputation (91 $Îź$s vs $\sim$500 ms). We address each inefficiency via existence checks, 32-byte SHA256 node references, zero-copy reference-counted buffers, and HashMap-based lexicographic deduplication. Benchmarks on Apple M1 Pro show 57\% heap allocation reduction (566,760 to 242,004 bytes per 10K proofs), parallel insertion at 2,433 ns/op, and network-wide elimination of 4.85 PB/year across 6,000 full nodes, advancing the Ethereum stateless roadmap.
Existing Decentralised Identifier (DID) methods require coordination, an agreed global order of operations, to update a DID document: blockchain-anchored methods incur fees and latency; lightweight peer methods (did:key, did:peer) offer no update mechanism; and Sidetree methods still require blockchain ordering for finality. We present did:crdt, a DID method that targets W3C DID Core and removes the need for coordination entirely: there is no ledger, no sequencer, and no global total order. Each DID document is composed of signed Conflict-Free Replicated Data Types (CRDTs), one per document field, each chosen so that concurrent edits merge deterministically. By the CALM Theorem, the state-merge path is then confluent: replicas that see the same updates reach the same document in any arrival order. The signed-delta path needs only causal delivery, applying an update after those it builds on, which is far weaker than the total ordering ledgers impose and needs no agreement protocol. We are explicit about scope: every untrusted-peer path is authenticated, so Byzantine fault tolerance (safety even when peers lie or send malformed data) holds for signed deltas and verified-bundle replay, while the unauthenticated state-merge path is a trusted-domain optimisation and key-compromise recovery is bounded by revocation semantics. We give the data and threat model, CRUD semantics, conflict resolution, and a Rust reference implementation with property-based convergence tests and microsecond-scale merge latency.
Data availability is a fundamental bottleneck in modern blockchain networks. Most blockchain systems rely on a full-replication model, which requires downloading of a full block to verify its availability. This model does not scale with block size because every node must handle large volumes of data, leading to slower block propagation, duplicated data transfer, and longer consensus agreement. This issue is well-known in Ethereum, where layer-2 rollups publish data directly into the chain. To overcome, Ethereum adopts Data Availability Sampling (DAS) to let nodes keep only a small fragment of the data while still ensuring availability. Prior work on DAS has focused on cryptographic foundations. Meanwhile, the peer-to-peer network layer that provides Byzantine-tolerant and scalable mechanisms for discovery and routing of DAS fragments is underexplored. We propose CDA, a new design for DAS based on coded distributed arrays that leverages network coding to ensure both robustness and efficiency. Our evaluation study compares CDA to RDA, the latest DAS development of Ethereum, showing an improvement of several times better.
Metode hybrid Autoregressive Integrated Moving Average dengan Support Vector Regression (ARIMA-SVR) merupakan salah satu metode untuk peramalan deret waktu yang mampu menangkap pola linear dan nonlinear secara bersamaan. Penelitian ini bertujuan menerapkan model hybrid ARIMA-SVR untuk meramalkan harga Ethereum dan mengetahui akurasi model hybrid ARIMA-SVR yang diperoleh pada harga Ethereum. Data yang digunakan yaitu data harga penutupan Ethereum pada rentang waktu 11 Desember 2020 sampai 10 Desember 2025, penelitian dimulai dengan membagi data menjadi data training dan data testing dengan tiga skema pembagian data yaitu 70%:10%, 80%:20%, dan 90%:10%. Hasil penelitian menunjukkan model terbaik yaitu ARIMA(2,1,2)-SVR dengan parameter terbaik sebesar 0.8125, parameter sebesar 5, dan parameter sebesar 0.125 pada skema pembagian data 90% data training dan 10% data testing. Akurasi model hybrid ARIMA(2,1,2)-SVR ditunjukkan oleh nilai Mean Absolute Percentage Error (MAPE) yang diperoleh yaitu 2.83% untuk data training dan 2.72% untuk data testing. Kata Kunci : ARIMA, SVR, Hybrid ARIMA-SVR, Ethereum The hybrid Autoregressive Integrated Moving Average with Support Vector Regression (ARIMA-SVR) method is a time series forecasting method capable of capturing both linear and nonlinear patterns simultaneously.This study aims to apply the ARIMA-SVR hybrid model to forecast Ethereum prices and determine the accuracy of the ARIMA-SVR hybrid model obtained for Ethereum prices. The data used consists of Ethereum closing prices from December 11, 2020, to December 10, 2025, the study began by dividing the data into training and testing sets using three data partitioning schemes is 70%:10%, 80%:20%, dan 90%:10%. The results indicate that the best model is the ARIMA(2,1,2)-SVR with optimal parameters = 0.8125, = 5, and = 0.125, under the 90% training dan 10% testing data split. The accuracy of the ARIMA(2,1,2)-SVR hybrid model is demonstrated by the Mean Absolute Percentage Error (MAPE) values obtained, which are 2.83% for the training data and 2.72% for the testing. Keywords : ARIMA, SVR, Hybrid ARIMA-SVR, Ethereum
Dustin Weiss, Robert Gaudiosi, Z. Ivy Zhou, Robert I. Webb
This paper examines intraday Bitcoin spot returns and trading activity around the expiration of Deribit Bitcoin options. Using data from spot exchanges and Deribit perpetual futures, we document a statistically and economically significant return reversal around expiration. The effect concentrates on days with elevated at-the-money open interest and is strongest when cumulative gamma exposure is negative, which is consistent with positive feedback trading pressure induced by option market makers hedging net short exposure. Trading activity also rises around expiry in Deribit perpetual futures and in the spot exchanges used to determine the Deribit settlement price. These intraday price effects are economically meaningful, implying annual wealth transfers of approximately USD 50 million between option writers and holders. Overall, the findings highlight the role of daily option expirations in shaping short-horizon price formation in Bitcoin markets and have implications for regulated investment products that rely on spot-market reference prices.
System and Method for Reinforcement LearningâBased Token Minting and CrossâChain Cryptographic Anchoring This archive contains the full nonâprovisional patent submission for a unified digitalâasset lifecycle system integrating reinforcementâlearningâbased token minting, Merkleâstructured ledgering, and synchronized crossâchain cryptographic anchoring. The invention establishes a deterministic, mathematically governed framework for creating, operating, and verifying digital asset states across heterogeneous blockchain networks including Bitcoin, Ethereum, and Solana. The system introduces a blueprintâbased binding mechanism, a formal kernel governed by a unified state equation, and a sovereign ledger enabling longâterm provenance and deterministic replay. A reversible 32âbyte commitment value is computed using a Spongeâ586 invariant and anchored to Bitcoin via Taproot tweaks and OP_RETURN payloads. Parallel anchoring events emit the authenticated Merkle Mountain Range (MMR) root on Ethereum and Solana, producing tamperâevident, multiâconsensus proofs of state. A reinforcementâlearning engine dynamically adjusts minting rates based on realâtime market conditions, behavioral metrics, and systemâlevel variables. The system further supports gasless user interactions (EIPâ2771), zeroâknowledge compliance pathways, federatedâlearning simulations, and deterministic state reconstruction through Kolmogorov integrity scoring and synthesis restoration. This archive includes the complete specification, mathematical formulations, alternative embodiments, and references to supporting research hosted on Zenodo. It documents the developmental lineage, reductionâtoâpractice demonstrations, and crossâchain anchoring methodology associated with U.S. Patent Application No. 19/693,343.
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Blockchain Technology Applications and Security
Intellectual Property and Patents
Physical Unclonable Functions (PUFs) and Hardware Security
A. B. Hajira Be A. B. Hajira Be, S.Bhuvaneshwari S.Bhuvaneshwari, Sankari.S Sankari.S
Cryptocurrency markets have gained significant global attention due to their decentralized nature and high financial value. Among various cryptocurrencies, Bitcoin is the most widely traded and exhibits highly volatile price behavior. Accurate analysis and prediction of Bitcoin price trends are challenging because the market is influenced by rapid trading activities, large data streams, and complex temporal patterns. This paper presents a streaming data collection and analysis system for Bitcoin using the Long Short-Term Memory (LSTM) deep learning algorithm. The proposed system continuously collects real-time Bitcoin market data from online cryptocurrency exchanges through streaming APIs. The collected data is then preprocessed and analyzed using an LSTM-based predictive model capable of learning long-term dependencies in time-series data. The LSTM network processes sequential historical price data to forecast future market trends and provide analytical insights into Bitcoin price movements. The system integrates data acquisition, preprocessing, deep learning-based prediction, and visualization modules to create an efficient cryptocurrency analysis framework. The proposed approach focuses on improving prediction accuracy by combining real-time streaming data with advanced neural network models. This system can assist researchers, financial analysts, and investors in understanding cryptocurrency market behavior and making informed trading decisions. The proposed design demonstrates the feasibility of integrating streaming data technologies with deep learning models for real-time financial market analysis. Keywordsâ Cryptocurrency, Bitcoin, Streaming Data, LSTM Algorithm, Deep Learning, Time-Series Prediction, Financial Data Analysis.
Abstract The rapid growth of decentralized AI applications has created a fundamental tension between computational integrity, model confidentiality, latency, and economic efficiency. Existing verification approaches, including zero-knowledge machine learning (zkML), optimistic machine learning (opML), and trusted execution environments (TEEs), provide strong guarantees along some dimensions but fail to simultaneously satisfy the practical requirements of large-scale AI inference systems deployed on blockchain infrastructure. This paper introduces AZR, a risk-adaptive verification architecture for decentralized AI inference on blockchain rollups. AZR dynamically selects among TEE attestation, optimistic fraud proofs, and zero-knowledge verification according to a query-specific risk function that captures economic value, adversarial exposure, and dispute likelihood. By allocating stronger verification mechanisms only to high-risk workloads, AZR balances security with operational efficiency while preserving computational integrity, model confidentiality, and input privacy. We formalize the verifier selection problem as a constrained optimization framework and analyze its security and economic properties under rational adversaries. Experimental evaluation across representative workloads, including ResNet-50, BERT-Base, and LLaMA-7B, demonstrates that AZR achieves substantial cost reductions relative to uniform zkML deployment while maintaining strong security guarantees. Under a representative workload distribution, AZR reduces verification costs by up to 61% compared with pure zkML systems, while enabling low-latency responses for the majority of inference requests. These results suggest that adaptive verification architectures provide a practical pathway toward scalable and trustworthy decentralized AI systems, bridging the gap between cryptographic assurance and the performance requirements of real-world blockchain applications.
This work presents a comprehensive study of entropy-based metrics for evaluating blockchain systems, focusing on on-chain ledger immutability, off-chain data integrity, and computational dynamics within blockchain virtual machines (BVMs). We develop a unified framework that models blockchain states as probabilistic distributions, quantifying uncertainty through Shannon entropy and examining its evolution under varying adversarial fractions. Extensive simulations demonstrate that on-chain entropy exhibits near-exponential decay, reflecting the cumulative reinforcement of honest consensus, while off-chain entropy remains static, highlighting the limitations of conventional data storage. Furthermore, the BVM is analyzed in terms of computation entropy, establishing its Turing completeness and demonstrating that smart-contract state evolution mirrors the information dynamics of arbitrary Turing machines. Our results provide quantitative evidence that entropy serves as both a theoretical and operational measure of immutability, tamper evidence, and protocol resilience. The proposed entropy framework offers practical tools for monitoring ledger integrity, detecting tampering, and assessing computational complexity, bridging the gap between information-theoretic principles and distributed ledger applications. This study advances both the theoretical understanding and practical evaluation of blockchain security, providing a principled methodology for analyzing distributed systems under adversarial conditions.
Abstract The modern single monetary real-value system suffers from long-term monetary alienation. Currency has evolved from a transaction tool into the ultimate target of wealth pursuit, triggering structural economic and social problems including capital hoarding, wealth polarization, economic involution, and class solidification. Based on the theoretical framework of The Symbiotic Order 1.0, this paper proposes a virtual-real dual-value hedging system consisting of currency and points. Without abolishing the existing monetary system or denying market division of labor and competition, the system establishes a positive-negative mirrored balance mechanism through the zero neutralization rule. The reverse hedging of currency income/expenditure and point increment/decrement eliminates the infinite hoarding attribute of currency and restores currency to its original instrumental positioning as a transaction medium. The system adopts a dual-track operation mechanism: the external monetary track encourages incremental economic expansion, technological progress and cultural export to maintain market vitality; the internal virtual-real hedging track reconstructs the allocation logic of stock resources and fundamentally restrains stock games and capital monopoly. Supported by basic point rules and cryptography technologies including homomorphic encryption and zero-knowledge proof, the system realizes rigid technical operation and avoids arbitrage by capital or power. This paper clarifies the institutional logic of competition motivation, verifying that the system corrects alienated monetary accumulation competition into original competition centered on experience right exchange, value creation and spiritual transcendence, rather than suppressing innovation and competition. Finally, it reflects on the institutional limitations and implementation thresholds. As a practical and targeted correction scheme for the dual contemporary dilemmas of capital concentration and nuclear deterrence deadlock, the system will become the optimal institutional choice when social predicaments reach critical thresholds. Key words: Symbiotic Order; virtual-real hedging; dual value system; monetary alienation; economic involution; institutional equilibrium
In [1], Kulenovi'c, Ladas and Overdeep posed a conjecture asserting that every positive solution of the rational second-order difference equation \[ y_{n+1}=\frac{y_n(1+y_n)^2}{y_n(1+y_n)+(1+y_{n-1})},\qquad n=0,1,\ldots, \] converges to a finite limit. We confirm this conjecture by deriving a short identity showing that the sign of $y_{n+1}-y_n$ is invariant with respect to $n$, so every positive solution is monotone. A simple estimate then gives an explicit initial-data-dependent upper bound in the increasing case, while the decreasing case is bounded below by positivity. Hence every positive solution converges. In addition, we introduce the auxiliary sequence \[ t_n:=\frac{y_n(1+y_n)}{1+y_{n-1}}, \] which is monotone in the direction opposite to that of $y_n$. It yields nested two-sided enclosures of the limit and an exact invariant-series formula. Writing $g_n=t_n-y_n$ and $\rho_n=t_n/(1+t_n)^2$, we prove that \[ I_n=y_n+g_n\sum_{j=0}^{\infty}\frac{1}{1+t_{n+j}} \prod_{m=0}^{j-1}\rho_{n+m} \] is independent of $n$ and satisfies $I_n=L=\lim_{k\to\infty}y_k$. Hence the limiting equilibrium selected by the initial data is determined by the invariant value $I_0$.
Cristhal Sther Sombra de Macedo, Ana ClĂĄudia Miranda Lopes Assis
In light of the datafication of the contemporary economy and the exponential growth in the production of intangible assets in the digital environment, there is a growing challenge to ensure the protection, integrity, and legal validity of these creations in a swift and accessible manner. Accordingly, the general objective of this article is to investigate whether blockchain technology, due to its properties of immutability, traceability, and timestamping, has the potential to be recognized as a reliable means of evidence for the protection of copyright and industrial property rights in Brazil. Using a deductive approach, through qualitative research and documentary and normative analysis, the study examines the compatibility of this technology with the Brazilian legal system. It investigates not only its potential to democratize access to evidence but also the regulatory, technical, and social obstacles that limit its widespread implementation. As a final consideration, it is understood that although blockchain is relevant for mitigating legal uncertainty and reducing barriers to access, its effectiveness is strictly complementary and does not replace formal state registration systems. Its full integration depends on overcoming regulatory gaps and digital inequalities.
A machine-checked, sorry-free formalization, in Lean 4 over Mathlib, of Sturm's theorem (1829): for a squarefree real polynomial p and an interval (a,b] whose endpoints are not roots, the number of distinct real roots of p in (a,b] equals V(a) â V(b), where V(x) is the number of sign changes of the Sturm sequence p, pâ˛, â(p mod pâ˛), ⌠evaluated at x (zeros discarded). No root is ever located; two integers are subtracted. The mathematics is entirely classical and the result has been formalized before in other systems (Coq, by Cohen, within the construction of the real algebraic numbers; Isabelle/HOL, by Eberl, and in the SturmâTarski form by Li and Paulson; and HOL Light). To the best of the author's knowledge â based on searches of Loogle and Mathlib in June 2026 â this is the first proof of Sturm's theorem in Lean; it is a first-in-Lean and not a first-in-any-system. The contribution is therefore the formalization itself together with its reusable machinery: a small theory of sign variation, an inductive flank-reduction relation (FlankReduce) that decouples the chain's combinatorics from its algebra, and the local-to-global passage from a single root crossing to the interval count. A by-product is that Mathlib's existing count of coefficient sign variations (Descartes' rule, Polynomial.signVariations) and the count used here are, after unfolding, the same function â so the toolkit transfers verbatim to Descartes. The headline theorem Sturm.sturm depends only on the three standard axioms propext, Classical.choice, Quot.sound; no native_decide and no custom axiom. The whole proof is a single file (Sturm.lean, about 1,220 lines, ~60 declarations) depending on Mathlib alone. Scope, stated plainly: the theorem is proved for squarefree p over the reals; the passage to p/gcd(p,pâ˛) for arbitrary polynomials is not formalized here. English and Spanish editions are included. Formalized with AI assistance (Claude, Anthropic); the mathematics and all claims are the author's responsibility, and the Lean kernel â not the assistant â certifies the proofs.